# Ejercicio 07.14

## Apartado a)

kill(all)$

load(draw)$
wxdraw2d(   
   grid = true,    line_type = solid,  line_width = 2, color = blue,
    implicit(3*x^3*y-y^4+5*x^2+5=0, x, -3.0,3.0, y, 0,4)
);

## Apartado b)

Eq1: 3*x^3*y-y^4+5*x^2+5=0;     depends(y,x);

diff(Eq1,x);

Eq2: -4*y^3*Dy(x)+3*x^3*Dy(x)+9*x^2*y+10*x=0;

Eq2b : subst ([x=1, y=2] , Eq2);

solve(Eq2b, Dy(1));

## Apartado c)

x1=x1:1$        y1=y1:2$        m=m:28/29$
y - y1 = m*(x - x1);
y - y1 = (-1/m)*(x - x1);

## Apartado d)

Eqd1: -4*y^3*('diff(y,x,1))+3*x^3*('diff(y,x,1))+9*x^2*y+10*x=0;

diff(Eqd1, x);

Eqd2:%;

diff(Eqd2, x);

Eqd3: -4*2^3*D2y(1)+3*1^3*D2y(1)-12*2^2*(28/29)^2+18*1^2*(28/29)+18*1*2+10=0;
solve(Eqd3, D2y(1));

Eqd4: -4*2^3*D3y(1)+3*1^3*D3y(1)-36*2^2*(28/29)*(15670/24389) + 
27*1^2*(15670/24389)-24*2*(28/29)^3+54*1*(28/29)+18*2=0;
solve(Eqd4, D3y(1));
solve(Eqd4, D3y(1)), numer;